The stability properties of a special family of parameter dependent nested hybrid multistep methods for stiff ODES

Abstract

In this paper, we analyses the stability properties of a special family of parameter dependent nested hybrid linear multistep methods (PDNHLMMs) for the numerical integration of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). Hybrid method is incorporating one or more off-step points for better stability properties. The stability properties of the method was investigated and the intervals of absolute stability of the methods of step number k ≤ 6 are determined using the boundary locus plot and the method is A- stable and A (α) –stable which makes the methods more suitable for stiff initial value problems.